Not really a valid comparison; learning languages and learning physical skills are very different. But you can run into the some of the same headaches. Ever cross up similar sounding words in the different languages? I speak English and Spanish; there's a lot of overlapping words, with differences in pronunciation and similar meanings -- and some that are quite different.
I see two main problems in learning two arts at once. One is simple: we all only have 24 hours in a day, and time spent on one thing is time not spent on another, so time spent on art A is time not spent on art B. Progress may slow... or not. Problem two only comes in if the arts are either very similar or very different in basis. If underlying principles are not going to be in harmony, you're going to have problems. If, say, one art is based on relaxation and no effort, and the other is based on maximum tension and effort... you might have trouble. Or if they're too similar, you might mix things up. I'll use Shotokan and TKD as an easy example, since most will agree that there's a good bit of linkage in the two arts. Or even two forms of karate... Now, you have to keep the kata and techniques and principles straight between them, or you'll be doing Pinan 1 when you should be doing Taeguk... (I hope I got the two paired right; please take the meaning rather than specifics, if not!)
Oh, and for the OP? Go out and do it, if you have the time and can afford it. I doubt you'll have trouble confusing BJJ and TKD!